Question: Simplify the following expression: $\sqrt{275}-\sqrt{176}+\sqrt{11}$
Solution: First, try to factor any perfect squares out of the radicals. $= \sqrt{275}-\sqrt{176}+\sqrt{11}$ $= \sqrt{25 \cdot 11}-\sqrt{16 \cdot 11}+\sqrt{11}$ Separate the radicals and simplify. $= \sqrt{25} \cdot \sqrt{11}-\sqrt{16} \cdot \sqrt{11}+\sqrt{11}$ $= 5\sqrt{11}-4\sqrt{11}+\sqrt{11}$ Finally, simplify by combining the terms. $= ( 5 - 4 + 1 )\sqrt{11} = 2\sqrt{11}$